I get asked this question a lot. Basically, it comes down to the major question of what you are going to be shooting. You could get all types of advice on filtration for optimal landscape shots but if that's not your focus then it's useless information. Some common filters include:

UV FILTER:
Buy one now and keep it on your lens if you don't already have one. Essentially, this is just a clear glass filter that protects your lens from the harmful UV rays from the sun but it also acts as a protection against scratches, etc. on your actual lens.

ND FILTERS:

Either .3 or .6 or .9 (1,2,3 stops respectively). If you are interested in achieving maximum shallow depth of field within the capabilities of the camera, NDs (Neutral Density) are a good choice. They will force you to open the iris more, allowing you to creatively focus on your subject when shooting medium to closeup shots. They will also help you keep the aperture at a sweet spot in terms of sharpness if you are shooting a bright light source. Closing the iris down tends to soften the picture and NDs help to alleviate that problem.

GRADUATED ND FILTERS:

Video is notorious for not having broad latitude. It will not smoothly transition from bright to dark and can "clip" very quickly, losing much detail in the process. This gives your shots a signature video look. If you are like me, this is not a good thing at all. If you are shooting vistas, a graduated ND filter is a great addition to your tool kit. These filters allow you to bring the contrast ratio between land and sky more into the range of what the camera can see. It will also allow you to capture pretty dramatic skies with plenty of cloud detail.

PROMIST/CLASSIC SOFT FILTERS:

These filters have the same effect as soft focus. Remember the women that Captain Kirk falls in love with on the original Star Trek? The DP would simulate that misty-eyed love struck moment by giving both Kirk and his love interest (particularly the latter) an exaggerated soft focus. These filters can also be used to hide skin blemishes and take the overall video harsh sharpness out of the picture. Summary: they soften the picture in a pretty way.

COLOR/SPECIAL EFFECTS FILTERS:
I personally stay away from these because I'm paranoid about getting a great shot and realizing that the effect ruins it because the effect is too much. I usually can achieve the same overall effect in post. There are many good uses for these kinds of filters but I would keep their use to a minimum. The novelty wears off very quickly for the viewer.

The exception to this is if you are shooting black and white. Many of these color filters (yellow, in particular) help to enhance contrast in your shots and make the black and white rendering much richer. There's plenty of info on the Web about creative black and white photography.

CIRCULAR POLARIZER:

Generally used to enhance the blue of a sky and make the clouds pop but it is also used to minimize reflections on windows and in water. In fact, a good quality polarizer can be very effective at removing unwanted reflections say if you are shooting through a car window, etc.

There are many more but that's all I can think of off the top of my head. Figure out what you are going to shoot and then determine what filters would work for you in your particular situation. 72mm circular filters that screw right on the front of the lens are much cheaper than 4x4 filters that fit in a mattebox but I don't recommend stacking a lot of filters directly on the lens.

Take a look at Tiffen's and Schneider's sites, they give good descriptions and some examples of how these filters work.